He have to pay $3.25.
Let the number of miles traveled by a driver be x
The toll paid by the driver is then represented as y. (in dollar)
Linear equation : an equation in which there is only one variable present. It is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution.
Since there is a linear relation between the two, we can assume the equation can be written as:
y = mx + c
From the given data, we get
0.24 = m(0) + c
c = 0.25
Using the second point:
1 = m(1) + 0.25
m = 1 − 0.25 = 0.75
Hence, the equation is y = 0.75x + 0.25.
If x = 4, then:
y = 0.75 × 4 + 0.25
y = 5.50
Hence, He have to pay $3.25.
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Help me with number 59 and 60 :)
Answer:
59. a₁ = 4
60. a₁ = 10
Step-by-step explanation:
The general equation for the sum of the first n terms Sₙ of a geometric sequence with common ratio r and first term a₁ is
[tex]S_n = a_1 \dfrac{1-r^n}{1-r}[/tex]
Problem 59
Here we are given
[tex]S_n = \dfrac{31}{4}\\\\r = \dfrac{1}{2}[/tex]
So we can plug these values into the above equation and get [tex]a_1[/tex]
Let's first compute [tex]1 - r^n[/tex]
[tex]1 - r^n = 1 - \left(\dfrac{1}{2}\right)^5\\\\\left(\dfrac{1}{2}\right)^5 = \dfrac{1}{32}\\\\1 - r^n = 1 - \left(\dfrac{1}{2}\right)^5 = 1-\dfrac{1}{32} = \dfrac{32}{32}-\dfrac{1}{32} = \dfrac{31}{32}[/tex]
[tex]1- r = 1 - \dfrac{1}{2} = \dfrac{1}{2}[/tex]
So
[tex]\dfrac{1-r^n}{1-r} = \dfrac{31}{32} \div \dfrac{1}{2} = \dfrac{31}{32} \times \dfrac{2}{1} = \dfrac{31}{16}[/tex]
Substituting this value into [tex]S_n = a_1 \dfrac{1-r^n}{1-r}[/tex] we get
[tex]\dfrac{31}{4} = a_1\dfrac{31}{16}[/tex]
Multiplying both sides by [tex]\dfrac{16}{31}[/tex]
[tex]\dfrac{31}{4} \times\dfrac{16}{31} = a_1\dfrac{31}{16} \times\dfrac{16}{31}\\\\4 = a_1 \textrm{or alternatively }\\ \\\boxed{a_1 = 4}[/tex]
Problem 60
Use the same technique as above
[tex]S_8 = 2550, r = 2\\\\S_8 = a_1 \times \dfrac{1-r^8}{1-r}\\\\\\2550 = a_1 \times \dfrac{1-2^8}{1-2}\\\\2550 = a_1 \times \dfrac{1 - 256}{1-2}\\\\2550 = a_1 \times \dfrac{-255}{-1}\\\\2550 = a_1 \times255\\\\== > a_1 = \dfrac{2550}{255}\\\\\boxed{a_1=10}[/tex]
15 Write an expression for the
gradient of the line
perpendicular to the line
segmentjoining
(3p, 6) to (-2p, 10).
5p/6 an expression for the gradient of the line perpendicular to the line segment joining (3p, 6) to (-2p, 10).
Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or the change in the y values over the change in the x values. The coordinates of the first point represent x1 and y1
gradient of the line segment joining (3p, 6) to (-2p, 10)
m=(y2-y1)/(x2-x1)
m =( 10 -4)/ ( -2p - 3p)
m= 6/ (-5p)
m= -6/5p
we know that
Gradient of a line perpendicular to a line with a gradient of m = -1/m
Gradient of a line perpendicular to a line with a gradient of -6/5p = 5p/6
Hence 5p/6 an expression for the gradient of the line perpendicular to the line segment joining (3p, 6) to (-2p, 10).
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define the points p(−4,−2) and q(3,−4). carry out the following calculation. find two vectors parallel to qp with length 4.
The vector is -2i+7j and the two parallel vectors with length 4 is u=-8/√53i+28/√53j and u=8/√53i-28/√53j respectively
The points are p(-4,-2) and q(3,-4)
The vector qp = vector p -vector q
qp= <-4+2,3+4>
qp=-2i+7j
|QP|=√(-2)^2+(7)^2
|QP|=√4+49
|QP|=√53
The unit vector in direction of QP is 1/√53(-2i+7j)
To get a unit vector parallel in direction of QP, multiply by 4
u=-8/√53i+28/√53j
Multiplying by -4 to get another parallel vector of length 4, we get
u=8/√53i-28/√53j
The term "parallel vectors" refers to 2 vectors which can be in the identical direction, have the equal attitude, but differ in magnitude.two vectors a and b are said to be parallel vectors if one is a scalar more than one of the opposite, the vectors could be parallel.Learn more about parallel vectors at:
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An expression is shown below.
2√51x
Which value of x makes the expression
equivalent to 10√51 ?
1. 6
2. 25
3. 59
4. 100
The required value of x in the expression 2√51x is 25.
Given that,
An expression 2√51x,
To determine the value of x when the expression is equivalent to 10√51.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
2√51x = 10√51
√51x = 5√51
√x = 5√51 / √51
√x = 5
squaring both sides
x = 25
Thus, the required value of x in the expression 2√51x is 25.
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home prices in a neighborhood vary every year. in 2021, the following nine home prices were listed. (in thousands)
H 120 166 173 H H H 123 127 L
Where L indicates a Home below $110 and H indicates a Home above $190. The median home price is:
A) 166
B) 169.5
C) 170
D) 173
E) Cannot be determined
Based on the prices of the homes in the neighborhood, the median home price is A) 166
What is the median home price?
L is for a home below $110 and H is for a home above $190. The distribution of home prices can therefore be shown as:
190, 120, 166, 173, 190, 190, 190, 123, 127, 110
In an ordered list, this becomes:
= 110, 120, 123, 127, 166, 173, 190, 190, 190
The median is the price in the middle and we can see this price is $166
In conclusion, the median home price is $166.
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Order the following numbers from least to greatest. Put the least number on the left. -0.32 -3.2 2 3|2
The numbers from least to greatest are arranged as -
-3.2, -0.32, 3/2, 2
What is ascending and descending order of arrangement of numbers?Ascending order is the arrangement of numbers from the smallest to the largest. For example, the following numbers are in ascending order: 3, 15, 28, 49. Descending order is an arrangement of numbers from the largest to the smallest. For example, the numbers 45, 32, 26, 12 are arranged in descending order.Given is the sequence of numbers as -
-0.32, - 3.2, 2, 3/2
The given sequence of numbers is -
-0.32, -3.2, 2, 3/2
The numbers from least to greatest are -
-3.2, -0.32, 3/2, 2
Therefore, the numbers from least to greatest are arranged as -
-3.2, -0.32, 3/2, 2.
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Monica reads 7 ½ pages of a mystery book in 5 minutes. What is her average reading rate in pages per minute?
Answer:
1.5 or 1 ½ pages per min
Step-by-step explanation:
7.5/5=1.5
She reads 1 ½ pages per min
Answer: 1.5 pages per minute
Step-by-step explanation:
Divide the total number of pages she read by 5, the amount of time it took her. So it should look like this: 7.5/5
The answer is 1.5 pages per minute.
18=2(4+x) ughhhh? omg
Step-by-step explanation:
linear
8+2x=18
2x=10
x=5
What is the quotient of 2 3/4 and 7/8?
Pls help fast
The quotient of the given expression 2 3/4 and 7/8 is 22/7
Quotient of an expressionQuotient refers to a number resulting from the division of one number by another. 12 ÷ 2 = 6 the quotient is 6
Dividend is number or expression that is to be divided by another. 12 ÷ 2 = 6 the dividend is 12
Divisor is the number or expression that is to be divided by another. 12 ÷ 2 = 6 the divisor is 2
Quotient of 2 3/4 and 7/8?
= 2 3/4 ÷ 7/8
= 11/4 ÷ 7/8
multiply by the reciprocal of 7/8= 11/4 × 8/7
= (11 × 8) / (4 × 7)
= 88/28
= 22/7
Therefore, the quotient of the given expression 2 3/4 and 7/8 is 22/7
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what is the parent function of () =− 2| − 3| + 1 ????
Answer:
|x|
Step-by-step explanation:
Review your parent functions and how to identify them. They are the fundamentals of algebra and pre calc
PLS HELP ASAP
DONT JUST USE FOR POINTS
WILL MARK BRAINLIST
ANSWER NEEDS TO BE CORRECT TYSM
THIS IS FROM IXL BTW
Answer:
6,720
Step-by-step explanation:
Answer:
31 square miles
Step-by-step explanation:
We basically have three shapes here.
The top rectangle:
A= l x w = 7 x 2 = 14
The middle rectangle:
A= l x w = 4 x 2 = 8
The triangle
A = 1/2 x b x h = (3 x 6)/2 = 18/2 = 9
Add the area of all three: 14 + 8 +9 = 31
if you have a mixture of 10 lb. sunflower seeds which cost 32c per pound and 16 lb. of cracked corn which cost 18¢per pound, how much would this mixture cost per pound?
By unitary method, we get that the total cost of mixture per pound = 50 cents.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Given:
Cost of 1 pound sunflower seeds = 32 cents.
Cost of 1 pound cracked corn = 18 cents.
Available sunflower seeds = 10lb = 10 pounds
Available cracked corn = 16lb = 16 pounds
To find: Cost of the mixture per pound
Finding:
By unitary method, Cost of 1 pound sunflower seeds = 32 cents.
Cost of 10 pounds sunflower seeds = 32(10) = 320 cents.
Again, by unitary method,
Cost of 1 pound cracked corn = 18 cents.
Cost of 16 pound cracked corn
= 18(16) cents
= 288 cents.
Therefore, total cost of mixture per pound
= 32 + 18 = 50 cents.
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alexio has $100$ cards numbered $1$-$100$, inclusive, and places them in a box. alexio then chooses a card from the box at random. what is the probability that the number on the card he chooses is a multiple of $2$, $3$ or $5$? express your answer as a common fraction.
Answer:
37/50
Step-by-step explanation:
You want the fraction of integers in the range [1, 100] that are divisible by 2, 3, or 5.
DivisibilityAttached is a Venn diagram showing how the divisibility of numbers from 1 to 100 stacks up. Circle A includes all 50 numbers divisible by 2; Circle B counts all 33 numbers divisible by 3; and Circle C counts the 20 numbers divisible by 5.
Where the circles overlap, there are counts of the numbers divisible by the relevant combination of factors. For example, there are 3 numbers divisible by 2, 3, and 5. (They are 30, 60, 90.)
ProbabilityIn all, there are 74 numbers in the range 1–100 that are divisible by 2, 3, or 5.
The probability that a card chosen at random will have a number divisible by 2, 3, or 5 is 74/100 = 37/50.
P( 2, 3, or 5 divides N) = 37/50.
__
Additional comment
Roughly, the number of numbers in range [A, B] divisible by n is (B -A)/n. This is how we arrived at the counts shown in the attachment. For example, There are 100/(2·5) = 10 numbers divisible by both 2 and 5. Of those, there are 10/3 = 3 divisible also by 3. So, the number 3 is found in the area ABC, and the number 10-3=7 is found in the area AB'C.
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terra writes the following proof for the theorem: if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram: terra's proof ao
Vertical angles or contrary angles are the statement that Terra's proof is still absent. The angles formed opposite to each other when two lines cross each other are equal.
The missing word in Terra's proof is described as :Terra describes the parallelogram nature of the diagram. Because they are vertical or opposite angles, these angles are equal.
The angles formed opposite to each other when two lines cross each other are equal. As a result, we have discovered that either vertical angles or opposite angles make up Terra's proof.
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The main courses at a restaurant all contain rice or onion. of the 23 choices, 17 contain onion and 14 contain rice. how many dishes contain both rice and onion?
If the main courses at a restaurant all contain rice or onion and of the 23 choices, 17 contain onion and 14 contain rice, then the number of dishes containing both rice and onion will be equal to 8.
The number of dishes that contain both rice and onion at the restaurant can be calculated by using an algebraic expression.
An algebraic expression can be defined as an equation in which both numerals and letters are present.
An algebraic expression for this problem can be given as,
(14 - x) + x + (17 - x) = 23
Here x is equal to the number of dishes containing both rice and onion.
14 + 17 - x + x - x = 23
31 - x = 23
x = 31 - 23
x = 8
Hence, the number of dishes that contain both rice and onion is calculated to be 8.
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Can someone please help me with this proof? I don't get how to do it.
2) BA and CD are parallel (segments that are collinear with parallel segments are parallel)
3) CDAB is a parallelogram (a quadrilateral with two pairs of parallel sides is a parallelogram)
4) ∠B is congruent to ∠D (opposite angles of a parallelogram are congruent)
5) m∠B = m∠D (congruent angles)
6) m∠D=115° (transitive property)
7) m∠EDA=65° (linear pair)
8) m∠EAD=65° (base angle of an isosceles triangle)
9) m∠E = 50° (sum of angles in a triangle)
Brandy and mark are selling magazines. Brandy has sold half as many as mark. Together they have sold 747 magazines. How many did each sell? Elimination
Answer 1120.5
Step-by-step explanation:
a fitness club with 100 members offers one free training session per member in either running, swimming, or weightlifting. Thirty of the fitness center members sign up for a free session. The running and swimming sessions are each twice as popular as the weightlifting session. What is the probability that a randomly chosen fitness club member signs up for a free running session?
The probability that a randomly chosen fitness club member signs up for a free running session is 0.4.
Let total s members sign up for the weightlifting session.
So, the total members for the running session is 2x.
And the total members for the swimming session be 2x.
Also here it is given that, thirty of the fitness center members sign up for a free session.
⇒ x + 2x + 2x = 30
⇒ 5x = 30
⇒ x = 30/5
⇒ x = 6
Thereofre, the probability that a randomly chosen fitness club member signs up for a free running session
= total number of members in running session/ number of members sign up for a free session
= 12/30
= 0.4
Hence, the probability that a randomly chosen fitness club member signs up for a free running session is 0.4.
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Please answer I need help
Answer:
What's the wildflowers trails current length so I can help
If 14 inches of wire cost 42 cents how many inches of wire can be bought with 21 cents
If 14 inches of wire cost 42 cents, with 21 cents can be bought 7 inch of wire
Information about the problem:
Inches bought= 14Inches bought cost = 42 centsAmount = 21 centsInches with 21 cents = ?Calculating how much 1 inch cost, we have:
1 inch cost= Inches bought cost / Inches bought
1 inch cost= 42 cents / 14 inches
1 inch cost= 3 cent/inch
Calculating how much can be bought with 21 cents:
Inches of wire= Amount / 1 inch cost
Inches of wire= 21 cent / 3 cent/inch
Inches of wire= 7 inch
What is a fraction?Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.
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1. J(1, 9), K(7, 4), L(8, 13), M(-2, 1)
The image of the points after they are reflected across the x-axis are J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)
How to determine the image of the points?From the question, we have the following parameters that can be used in our computation:
J(1, 9), K(7, 4), L(8, 13), M(-2, 1)
Also from the question we have the transformation to be
Transformation: reflection across the x-axis
The rule of the reflection across the x-axis is represented as
(x, y) = (x, -y)
Substitute the known values J(1, 9), K(7, 4), L(8, 13), M(-2, 1) in the above equation, so, we have the following representation
J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)
Hence, the image of the points are J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)
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Find the equation of the linear function represented by the table below in slope-intercept form.
The equation of the linear function represented by the table below in slope-intercept form is y = 7x + 4
Linear equationsThe equation of a line in point-slope form is expressed as y = mx + b
where
m is the slope
b is the intercept
Using the coordinate points (0,4) and (1, 11)
Slope = 11-4/1-0
slope = 7
The y-intercept is at the point (0,4)
Determine the equation
y = mx + b
y = 7x + 4
Hence the equation of the linear function represented by the table below in slope-intercept form is y = 7x + 4
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4(5x+3)=14x+30 not sure if i understand
Answer:
x = 3
Step-by-step explanation:
Use the distributive property to multiply 4 by 5x+3. Subtract 14x from both sides. Combine 20x and −14x to get 6x. Subtract 12 from both sides. Subtract 12 from 30 to get 18. Divide both sides by 6. Divide 18 by 6 to get 3.
Answer:
20x+12=14x+30
6x=18
x=3
Step-by-step explanation:
First, apply the distributive property:
4(5x+3) = 4 · 5x + 4 · 3 = 20x+12
Now, we have this equation
20x+12=14x+30
We need to group the elements now.
So, to bring all the elements with an "x," we subtract 14x from both sides.
20x-14x+12=14x+30-14x
We have this now
6x+12=30
Now, let's subtract 12 on both sides
6x+12-12=30-12
6x=18
Divide both sides by 6
x=3
i need helpppppppppp
Answer: XYW = 32, WYZ = 85
Step-by-step explanation:
We are looking for what x is, which we can find with the formula:
117 = (6x+44) + (-10x+65)
117 = -4x + 109
8 = -4x
x = -2
We can verify this is correct by plugging it in and seeing if they add up to 117.
6x + 44 (XYW)
= 6(-2) + 44
= -12 + 44
= 32
-10x + 65 (WYZ)
= -10(-2) + 65
= 20 + 65
= 85
32 + 85 = 117
6.018 to 1 decimal place
Answer:
6.0
Step-by-step explanation:
Answer:
Step-by-step explanation:
1.00
What is the slope of the line that passes through the points (6,10) and (6,−2)? Write your answer in simplest form.
The slope of the line passes through the points (6,10) and (6,−2) is undefined.
Here,
The points are (6,10) and (6,−2).
We have to find the slope of the line passes through the points (6,10) and (6,−2).
What is slope of line?
The slope of the line passes through the points (x₁, y₁) and (x₂, y₂) is;
[tex]m = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
Now,
The points are (6,10) and (6,−2).
Hence, The slope of the line passes through the points (6,10) and (6,−2) is;
[tex]m = \frac{-2 -10 }{6-6 }= \frac{-12}{0}[/tex]
Which in undefined.
Therefore, The slope of the line passes through the points (6,10) and (6,−2) is undefined.
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the slope of the line that passes through the points (6,10) and (6,−2) is undefined.
Step-by-step explanation:
Slopes of perpendicular lines are equal. true or false
False, parallel lines have not the same slope whereas perpendicular lines have because of this. Perpendicular lines have equal slopes.
What is a slope in mathematics?The steepness and direction of a line, read from left to right, is referred to as its slope. Finding the ratio of will allow you to determine the slope or gradient. Between two places on the line, either by using the rise (vertical change) to the run (horizontal change). a slope-intercept version of a linear equation (y = mx + b).
based on the facts provided;
Two parallel lines' slopes are always their negative reciprocal of one another. The other has a slope of -3/2 if one has a slope of 2/3.
Therefore, perpendicular lines do not have equal slopes.
The sentence is
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Is the following relation a function? x y 1 4 −1 −2 3 10 5 16 a Yes b No
The relation that is represented in the table is a function. YES.
How to Determine a Relation that is a Function?For every relation that represents a function, the each of the x-value (domain element/input) corresponds to exactly one y-value (range element/output).
In the table given showing a relation, every single x-value (input) has exactly only one possible y-value (output) that it is assigned to. The x-values, 1, -1, 3, and 5, each have a specific y-value they each correspond to.
Thus, based on the definition of a function, the relation that is represented in the table is a function. YES.
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the sum of two numbers is 16 and their diffrence is 14
Answer:
15, 1
Step-by-step explanation:
I'm assuming the answer should be limited to only positive integers. Either way, looking at 16 and 14, they are 2 apart and their average is 15. Since 15 is one from 16 and 14 both, the answer is 15 and 1.
15-1 = 14
15+1 = 16
ANSWER QUICK PLS
Follow the steps to solve 15 / 4 – (-41/3)
a. Rewrite as addition
b. State whether the answer will be positive or negative
c. Solve